<p>The Mechanics of Structural Genome (MSG) is a unified homogenization theory used to find equivalent constitutive models for beam, plate, and solid structures. It has been proven accurate for periodic structures. However, for certain applications such as non-prismatic wind turbine blades and helicopter flexbeams featuring ply drop-off, where there is no repeating structure and the periodic boundary condition cannot be used, MSG's accuracy is limited. In this work, we aim to extend MSG to find element stiffness matrices directly for aperiodic structures, instead of beam properties or three-dimensional (3D) solid material properties. Two finite elements based on MSG have been developed: Heterogeneous Beam Element (HBE) and Heterogeneous Solid Element (HSE).</p> <p><br></p> <p>For beam modeling, the beam-like structure is homogenized into a series of 3-node Heterogeneous Beam Elements (HBE) with 18×18 effective beam element stiffness matrices. These matrices are used as input for one-dimensional (1D) beam analysis using the Abaqus User Element subroutine (UEL). Using the macroscopic beam analysis results as input, we can also perform dehomogenization to predict the stresses and strains in the original structure. We use three examples (a prismatic composite beam, an isotropic homogeneous tapered beam, and a composite tapered beam) to demonstrate the capability of HBE and show its advantages over the MSG cross-sectional analysis approach. HBE can capture macroscopic behavior and detailed stresses due to non-prismatic geometry.</p> <p><br></p> <p>The Heterogeneous Solid Element (HSE) is developed based on MSG to model a heterogeneous body as an equivalent solid element using an effective element stiffness matrix. HSE modeling includes homogenization, macroscopic global analysis, and dehomogenization to recover local strains/stresses. HSE avoids the local periodicity assumption for traditional multiscale modeling techniques for composite structures that compute effective material properties instead. Abaqus composite solid element and MSG-based traditional multiscale modeling are used to validate the accuracy of HSE. All example results show that HSE is more accurate in predicting global structural behavior and local strains/stresses.</p> <p><br></p> <p>HBE and HSE provide a new concept for modeling aperiodic composite structures by modeling structures into equivalent beam or solid elements instead of beam properties of the reference line in 1D beam analysis or material properties of material points in solid structural analysis.</p>

<p>Extrusion Deposition Additive Manufacturing (EDAM) is a process in which fiber-filled thermoplastic polymers pellets get molten in the extruder and deposited onto a build plate in a layer-by-layer basis. The use of short fiber composite for EDAM has enabled large-scale 3D printing structures and tools for traditional composite manufacturing processes. Successful EDAM production critically depends on the understanding of the process-structure-property relationship. Especially on the bonding between the beads which is of paramount importance in additive manufacturing since it affects primarily the fracture and strength characteristics of the printed part. Bonding is influenced mainly by the temperature history and the contact between the beads. Both of which is dependent on the fiber orientation within the bead induced by the flow deformation that occurs according to the printing parameters. This study aims to investigate and model the complex relationship between the printing conditions and inter-bead bonding in the lateral direction.</p> <p>A framework was developed to facilitate this aim, and it contains a fusion bonding model that couples the time-temperature history and the bead-to-bead contact interface. Four deposition parameters were studied: the nozzle height, ratio of the print velocity to extrudate velocity, bead-to-bead spacing, and layer time. First, a deposition flow model was developed, utilizing the anisotropic viscous flow model and smooth particle hydrodynamic finite element formulation, to predict the fiber orientation state across the deposited bead and the bead-to-bead interface for the given set of deposition parameters. Next, the effect of printing conditions on the temperature history of the bead was discovered by utilizing the heat transfer process simulation in ADDITIVE3D. Third, the experimental characterization procedure for mode I fracture toughness in the lateral direction was developed, and the fracture toughness was characterized using linear elastic fracture mechanics principles. Lastly, the phenomenological model for non-isothermal lateral fusion bonding was characterized using the bead contact interface, temperature history, and fracture toughness properties. This work showed a comprehensive effort in fusion bonding modeling while also presented a valuable process-structure-property-performance relationship in EDAM.  Guidance on the selection of printing conditions and strategy can be made using the developed model to print higher-strength parts.  </p>

<div>As the use of fiber-reinforced polymer composites grows in aerospace structures, there is an emerging need to implement damage tolerant approaches. The use of <i>in-situ</i> synchrotron X-ray tomography enables direct observations of progressive damage relative to the microstructural features, which is studied in a T650/5320 laminate composite with varying layup orientations (using 45^o and -45^o plies) in a compact tension specimen geometry. Specifically, the interactions of micromechanical damage mechanisms at the notch tip were analyzed through 3D image processing as the crack grew. First, monotonic tests were conducted where X-ray tomography was acquired incrementally between the unloaded state and maximum load. The analysis of the monotonic tension specimens showed intralaminar cracking was dominant during crack initiation, delamination became prevalent during the later stages of crack progression, and fiber breakage was, in general, largely related to intralaminar cracking. After the monotonic tension analysis, modifications were made to the specimen geometry and the loading assembly, and fatigue tests were conducted, also using <i>in-situ</i> synchrotron X-ray tomography. Specifically, tomography images were acquired after select intervals of cyclic loading to examine the crack growth behavior up to 5802 cycles. The analysis of the fatigue tests showed that intralaminar cracking was also dominant, while localized delamination allowed ply cross-over. A finite element analysis was conducted by comparing the crack profile at varying intervals of loading, and the change in stored energy per cycle, dU/dN, was calculated. The combined experimental and simulation analysis showed that when the per ply values of dU/dN were examined, the intralaminar cracking rate collapsed to one curve regardless of the ply orientation, where direct observations of fiber bridging were characterized and associated with a reduction in crack growth rate for the influenced ply. Overall, this work provides a physical understanding of the micromechanics facilitating intralaminar crack growth in composites, providing engineers the necessary assessments for slow crack growth approaches in structural composite materials.<br></div>

<p dir="ltr">The demand and utilization of fiber-reinforced composites are increasing in various sectors, including aerospace, civil engineering, and automotive industries. Non-destructive methods are necessary for monitoring fiber-reinforced composites due to their complex and often visually undetectable failure modes. An emerging method for monitoring composite structures is through the integration of self-sensing capabilities. Self-sensing in nanocomposites can be achieved through nanofiller modifications, which involve introducing an adequate amount of nanofillers into the matrix, such as carbon nanotubes (CNTs) and carbon nanofillers (CNFs). These fillers form an electrically well-connected network that allows the electrical current to travel through conductive pathways. The disruption of connectivity of these pathways, caused by mechanical deformations or damages, results in a change in the overall conductivity of the material, thereby enabling intrinsic self-sensing.</p><p dir="ltr">Currently, the majority of predictive modeling attempts in the field of self-sensing nanocomposites have been dedicated to microscale piezoresistivity. There has been a lack of research conducted on the modeling of strain-induced resistivity changes in macroscale fiber-matrix material systems. As a matter of fact, no analytical macroscale model that addresses the impact of continuous fiber reinforcement in nanocomposites has been presented in the literature. This gap is significant because it is impossible to make meaningful structural condition predictions without models relating observed resistivity changes to the mechanical condition of the composite. Accordingly, this dissertation presents a set of three research contributions. The overall objective of these contributions is to address this knowledge gap by developing and validating an analytical model. In addition to advancing our theoretical understanding, this model provides a practical methodology for predicting the piezoresistive properties of continuous fiber-reinforced composites with integrated nanofillers.</p><p dir="ltr">To bridge the above-mentioned research gap, three scholarly contributions are presented in this dissertation. The first contribution proposes an analytical model that aims to predict the variations in resistivity within a material system comprising a nanofiller-modified polymer and continuous fiber reinforcement, specifically in response to axial strain. The fundamental principle underlying our methodology involves the novel use of the concentric cylindrical assembly (CCA) homogenization technique to model piezoresistivity. The initial step involves the establishment of a domain consisting of concentric cylinders that represent a continuous reinforcing fiber phase wrapped around by a nanofiller-modified matrix phase. Subsequently, the system undergoes homogenization to facilitate the prediction of changes in the axial and transverse resistivity of the concentric cylinder as a consequence of longitudinal deformations. The second contribution investigates the effect of radial deformations on piezoresistivity. Here, we demonstrate yet another novel application of the CCA homogenization technique to determine piezoresistivity. This contribution concludes by presenting closed-form analytical relations that describe changes in axial and transverse resistivity as functions of externally applied radial strain. The third contribution involves computationally analyzing piezoresistivity in fiber-reinforced laminae by using three-dimensional representative volume elements (RVE) with a CNF/epoxy matrix. By comparing the single-fiber-based analytical model with the computational model, we can investigate the impact of interactions between multiple adjacent fibers on the piezoresistive properties of the material. The study revealed that the differences between the single-fiber CCA analytical model and the computational model are quite small, particularly for composites with low- to moderate-fiber volume fractions that undergo relatively minor deformations. This means that the analytical methods herein derived can be used to make accurate predictions without resorting to much more laborious computational methods.</p><p dir="ltr">In summary, the impact of this dissertation work lies in the development of novel analytical closed-form nonlinear piezoresistive relations. These relations relate the electrical conductivity/resistivity changes induced by axial or lateral mechanical deformations in directions parallel and perpendicular to the reinforcing continuous fibers within fiber-reinforced nanocomposites and are validated against in-depth computational analyses. Therefore, these models provide an important and first-ever bridge between simply observing electrical changes in a self-sensing fiber-reinforced composite and relating such observations to the mechanical state of the material.</p>

<p>Composite materials have been invented and used to make all kinds of industrial products, such as automobiles, aircraft, sports equipment etc., for many years. Excellent properties such as high specific stiffness and strength have been recognized and studied for decades, motivating the use of composite materials. However, the design of composite structures still remains a challenge. Existing design tools are not adequate to exploit the full benefits of composites. Many tools are still based on the traditional material selection paradigm created for isotropic homogeneous materials, separated from the shape design. This will lose the coupling effects between composite materials and the geometry and lead to less optimum design of the structure. Hence, due to heterogeneity and anisotropy inherent in composites, it is necessary to model composite parts with appropriate microstructures  instead of simplistically replacing composites as black aluminum and consider materials and geometry at the same time.</p> <p><br></p> <p>This work mainly focuses on the design problems of complex material-structural systems through computational analyses. Complex material-structural systems are structures made of materials that have microstructures smaller than the overall structural dimension but still obeying the continuum assumption, such as fiber reinforced laminates, sandwich structures, and meta-materials, to name a few. This work aims to propose a new design-by-analysis framework based on the mechanics of structure genome (MSG), because of its capability in accurate and efficient predictions of effective properties  for different solid/structural models and three-dimensional local fields (stresses, strains, failure status, etc). The main task is to implement the proposed framework by developing new tools and integrating these tools into a complete design toolkit. The main contribution of this work is a new efficient high-fidelity design-by-analysis framework for complex material-structural systems.</p> <p><br></p> <p>The proposed design framework contains the following components. 1) MSG and its companion code SwiftComp is the theoretical foundation for structural analysis in this design framework. This is used to model the complex details of the composite structures. This approach provides engineers the flexibility to use different multiscale modeling strategies. 2) Structure Gene (SG) builder creates finite element-based model inputs for SwiftComp using design parameters defining the structure. This helps designers deal with realistic and meaningful engineering parameters directly without expert knowledge of finite element analysis. 3) Interface is developed using Python for easy access to needed data such as structural properties and failure status. This is used as the integrator linking all components and/or other tools outside this framework. 4) Design optimization methods and iteration controller are used for conducting the actual design studies such as parametric study, optimization, surrogate modeling, and uncertainty quantification. This is achieved by integrating Dakota into this framework. 5) Structural analysis tool is used for  computing global structural responses. This is used if an integrated MSG-based global analysis process is needed.</p> <p><br></p> <p>Several realistic design problems of composite structures are used to demonstrate the capabilities of the proposed framework. Parameter study of a simple fiber reinforce laminated structure is carried out for investigating the following: comparing with traditional design-by-analysis approaches, whether the new approach can bring new understandings on parameter-response relations and because of new parameterization methods and more accurate analysis results. A realistic helicopter rotor blade is used to demonstrate the optimization capability of this framework. The geometry and material of composite rotor blades are optimized to reach desired structural performance. The rotor blade is also used to show the capability of strength-based design using surrogate models of sectional failure criteria. A thin-walled composite shell structure is used to demonstrate the capability of designing variable stiffness structures by steering in-plane orientations of fibers of the laminate. Finally, the tool is used to study and design auxetic laminated composite materials which have negative Poisson's ratios.</p>

<p>With the emergence of additive manufacturing (AM), there is a need to understand the role of microstructures resulting from AM on the mechanical performance of the material. Ti-6Al-4V alloys are widely used within the aerospace industry as well as other industries to achieve high strength, low weight premium performance parts. There is a desire to utilize AM to produce Ti-6Al-4V, although these materials need to be qualified prior to their use in safety critical applications. Within the qualification of AM Ti-6Al-4V in aeronautics, fatigue loading is a crucial aspect to. It has been seen that within AM Ti-6Al-4V, prior β boundaries can be locations of microscopic localization of plastic strain which often lead to fatigue crack initiation. This thesis aims to further understand and predict the role of AM Ti-6Al-4V microstructures in dictating fatigue behavior. Specifically, the goal was to gauge the contributions of two microstructural features resulting from AM, prior β boundaries and α lathe-shaped grains, to the localization behavior. With the need to understand and predict the emergent behavior of the material system, crystal plasticity finite element (CPFE) methods were used in this thesis as the main method. </p> <p><br></p> <p>Within the context of CPFE, there is an existing gap in the current literature of realistic synthetic microstructures of Ti-6Al-4V that capture both the prior β boundaries and α lathes. With the ability to generate realistic FE models, the effects of the microstructural features can be better studied and characterized. The first portion of this thesis focuses on the generation of such synthetic microstructures which are simulated within the CPFE framework. An emphasis is placed on modeling the prior β boundaries and α grains. As these generated models are statistically equivalent to actual microstructures, material characterization via EBSD was performed on specimen that were used in the experimental fatigue testing. With the framework’s ability to generate synthetic microstructures that consider one prior β grain or multiple β grains (and thus prior β boundaries), simulations were conducted on both conditions of microstructures. </p> <p><br></p> <p>In the second portion of this thesis, simulations are conducted on two conditions of synthetic microstructures: models which contain 𝛼 lathes associated with one prior 𝛽 grain and models which contain multiple prior 𝛽 boundaries and the respective 𝛼 lathes. The goals of the simulations included: (1) lifing the different synthetic microstructures using a fatigue lifing model by way of the accumulated plastic strain energy density (APSED), (2) analyzing the microscopic localization of APSED at the prior β boundaries, and (3) analyzing the effects of the α lathes on the microscopic localization. This investigation aimed to further shed light on the effects of the additive manufacturing process and the implications of the resulting microstructure on the fatigue properties of AM Ti-6Al-4V. Furthermore, physics-based prognosis strategies similar to what is employed here will enable the rapid qualification of materials/structures and the ability to tailor component design on fatigue performance. </p>

<div>Defects are unavoidable, life-limiting and dominant sites of damage and subsequent failure in a material. Ni-based superalloys are commonly used in high temperature applications and inevitably found to have defects in the form of inclusions, voids and microscopic cracks which are below the resolution of standard inspection techniques. A mechanistic understanding of the role of defects in such industrially relevant bulk polycrystalline material is essential for philosophies of design and durability to follow and ensure structural integrity of components in the inevitable presence of such defects. The current understanding of defect-mediated damage, in bulk Ni superalloys, is limited by experimental techniques that can capture the local micromechanical state of the material surrounding the defect. In this work, we combine mechanical testing with in-situ, non-destructive 3-D X-ray characterization techniques to obtain rich multi-modal datasets at the microscale to interrogate complex defect-microstructure interactions and elucidate the mechanisms of failure around defects. The attenuated X-ray beam, after passage through the material, is utilized through computed micro-tomography to characterize the defects owing to its sensitivity to density differences in the material. The diffracted X-ray beam, after illuminating the material, is employed through high energy diffraction microscopy in various modes to interrogate the evolving micromechanical state around the discovered defects.</div><div>Three case studies are performed with specimens made of a Ni-based superalloy specially designed and fabricated to have internal defects in the form of: (i) an inclusion, (ii) a microscopic crack, and (iii) voids. In each case, the grain scale information is investigated to reveal heterogeneity in the local micromechanical state of the material as a precursor for the onset of failure. Models and simulations based on finite element or crystal plasticity are utilized, wherever necessary, to assess the factors essential to the underlying mechanism of failure. In the first case study, the detrimental effects of an inclusion in initiating a crack upon cyclic loading is interrogated and the state of bonding, residual stresses, and geometrical stress concentrations around the inclusion are demonstrated to be of utmost importance. In the second case study, the propagation of a short fatigue crack through the microstructure is examined to reveal the crystallographic nature of crack growth through the (i) alignment of the crack plane with the most active slip system, (ii) the correlation between the crack growth rate and the maximum resolved shear stresses, and (iii) the dependence of the crack growth direction on microplasticity within grains ahead of the crack front. In the third case study, the role of voids in ductile failure under tensile loading is explored to illuminate the activation and operation of distinct mechanisms of inter-void shear and necking under the control of the local state of stress triaxiality and the local plasticity within the grains at critical sites of fracture.</div><div>In summary, a grain scale description of the micromechanical state has been unambiguously determined through experiments to examine the heterogeneity around defects in the material. It has enabled us to identify and isolate the nature of factors essential to the activation of specific mechanisms at the onset failure. The grain scale thus provides an ideal physical basis to understand the fundamentals of defect mediated damage and failure instilling trust in the predictive capabilities of models that incorporate the response of the grain structure. The generated datasets can be used to instantiate and calibrate such models at the grain level for higher fidelity. </div>

Computational modeling is essential for material and structural analyses for a multitude of reasons, including for the improvement of design and reducing manufacturing costs. However, the cost of commercial finite element packages prevent companies with limited financial resources from accessing them. Free finite element solvers, such as Warp3D, exist as robust alternatives to commercial finite element analysis (FEA) packages. This and other open-source finite element solvers are not necessarily easy to use. This is mainly due to a lack of a preprocessing framework, where users can generate meshes, apply boundary conditions and forces, or define materials. We developed a preprocessor for Warp3d, which is referred to as <i>W3DInput</i>, to generate input files for the processor. <i>W3DInput</i> creates a general framework, at no cost, to go from CAD models to structural analysis. With this preprocessor, the user can import a mesh from a mesh generator software – for this project, Gmsh was utilized – and the preprocessor will step the user through the necessary inputs for a Warp3D file. By using this preprocessor, the input file is guaranteed to be in the correct order and format that is readable by the solver, and makes it more accessible for users of all levels. With this preprocessor, five use cases were created: a cantilever beam, a displacement control test, a displacement control test with a material defined by a user-defined stress-strain curve, a crystal plasticity model, and pallet. Results were outputted to Exodus II files for viewing in Paraview, and the results were verified by checking the stress-strain curves. Results from these use cases show that the input files generated from the preprocessor functions were correct.

Among the many active materials in use today, piezoelectric composite patches have enabled notable advances in emerging technologies such as disturbance sensing, control of flexible structures, and energy harvesting. The macro fiber composite (MFC), in particular, is well known for its outstanding performance. Multiscale models are typically required for smart-structure design with MFCs. This is due to the need for predicting the macroscopic response (such as tip deflection under a transverse load or applied voltage) while accounting for the fact that the MFC has microscale details. Current multiscale models of the MFC exclusively focus on predicting the macroscopic response with homogenized material properties. There are a limited number of homogenized properties available from physical experiments and various aspects of existing homogenization techniques for the MFC are shown here to be inadequate. Thus, new homogenized models of the MFC are proposed to improve smart-structure predictions and therefore improve device design. It is notable that current multiscale modeling efforts for MFCs are incomplete since, after homogenization, the local fields such as stresses and electric fields have not been recovered. Existing methods for obtaining local fields are not applicable since the electrodes of the MFC are embedded among passive layers. Therefore, another objective of this work was to find the local fields of the MFC without having the computational burden of fully modeling the microscopic features of the MFC over a macroscale area. This should enable smart-structure designs with improved reliability because failure studies of MFCs will be enabled. Large-scale 3D finite element (FE) models that included microscale features were constructed throughout this work to verify the multiscale methodologies. Note that after creating a free account on cdmhub.org, many files used to create the results in this work can be downloaded from https://cdmhub.org/projects/ernestocamarena.<br><br>First, the Mechanics of Structure Genome (MSG) was extended to provide a rigorous analytical homogenization method. The MFC was idealized to consist of a stack of homogeneous layers where some of the layers were homogenized with existing rules of mixtures. For the analytical model, the electrical behavior caused by the interdigitated electrodes (IDEs) was approximated with uniform poling and uniform electrodes. All other assumptions on the field variables were avoided; thus an exact solution for a stack of homogeneous layers was found with MSG. In doing so, it was proved that in any such multi-layered composite, the in-plane strains and the transverse stresses are equal in each layer and the in-plane electric fields and transverse electric displacement are constant between the electrodes. Using this knowledge, a hybrid rule of mixtures was developed to homogenize the entire MFC layup so as to obtain the complete set of effective device properties. Since various assumptions were avoided and since the property set is now complete, it is expected that greater energy equivalence between reality and the homogenized model has been made possible. The derivation clarified what the electrical behavior of a homogenized solid with internal electrodes should be—an issue that has not been well understood. The behavior was verified by large-scale FE models of an isolated MFC patch.<br> <br>Increased geometrical fidelity for homogenization was achieved with an FE-based RVE analysis that accounted for finite-thickness effects. The presented theory also rectifies numerous issues in the literature with the use of the periodic boundary conditions. The procedure was first developed without regard to the internal electrodes (ie a homogenization of the active layer). At this level, the boundary conditions were shown to satisfy a piezoelectric macrohomogeneity condition. The methodology was then applied to the full MFC layup, and modifications were implemented so that both types of MFC electrodes would be accounted for. The IDE case considered nonuniform poling and electric fields, but fully poled material was assumed. The inherent challenges associated with these nonuniformities are explored, and a solution is proposed. Based on the homogenization boundary conditions, a dehomogenization procedure was proposed that enables the recovery of local fields. The RVE analysis results for the effective properties revealed that the homogenization procedure yields an unsymmetric constitutive relation; which suggests that the MFC cannot be homogenized as rigorously as expected. Nonetheless, the obtained properties were verified to yield favorable results when compared to a large-scale 3D FE model.<br> <br>As a final test of the obtained effective properties, large-scale 3D FE models of MFCs acting in a static unimorph configuration were considered. The most critical case to test was the smallest MFC available. Since none of the homogenized models account for the passive MFC regions that surround the piezoelectric fiber array, some of the test models were constructed with and without the passive regions. Studying the deflection of the host substrate revealed that ignoring the passive area in smaller MFCs can overpredict the response by up to 20%. Satisfactory agreement between the homogenized models and a direct numerical simulation were obtained with a larger MFC (about a 5% difference for the tip deflection). Furthermore, the uniform polarization assumption (in the analytical model) for the IDE case was found to be inadequate. Lastly, the recovery of the local fields was found to need improvement.<br><br><br>

First, the theory of MSG is extended to aperiodic heterogeneous solid structures. Integral constraints are introduced to decompose the displacements and strains of the heterogeneous material into a fluctuating part and a macroscopic part, of which the macroscopic part represents the responses of the homogenized material. One advantage of this theory is that boundary conditions are not required. Consequently, it is capable of handling micro-structures of arbitrary shapes. In addition, periodic constraints can be incorporated into this theory as needed to model periodic or partially periodic materials such as textile composites. In this study, the newly developed method is employed to investigate the finite thickness effect of textile composites.<div><br></div><div>Second, MSG is enabled to deal with Timoshenko beam-like structures with spanwise heterogeneity, which provide higher accuracy than the previous available Euler–Bernoulli beam model. Its reduced form, the MSG beam cross sectional analysis, is found to be able to analyze generalized free-edge problems with arbitrary layups and subjected to general loads. In this method, the only assumption applied is that the laminate is long enough so that the Saint-Venant principle can be adopted. There is no limitation on the cross section of the laminate since no ad hoc assumption is involved with the microstructure geometry. This method solve the free-edge problem from a multiscale simulation point of view.<br></div><div><br></div>